1. Field of the Invention
The present invention relates to a manufacturing method for obtaining a single electron transistor by electro-migration of nanocluster.
More specifically, the invention relates to a method for manufacturing a single electron transistor by electro-migration of nanocluster
2. Description of the Related Art
To fully understand all the aspects of the present invention reference is made to the enclosed FIGS. 1-4 showing known examples of single-electron devices.
The enclosed FIG. 1 illustrates the basic concept of single-electronics.
Let's first consider a small electroneutral conductor, traditionally called an island, having exactly as many (m) electrons as protons in its crystal lattice.
In this electroneutral state the island does not generate any appreciable electric field beyond its borders, and a even weak external force {right arrow over (F)} may bring in an additional electron from outside. In most single-electron devices, this injection is carried out by a tunneling effect through an energy barrier created by a thin insulating layer. Now, after this injection, the net charge Q of the island would be (−e), and the resulting electric field E would repulse any further electron that might be added.
Though the fundamental charge is very small in absolute value (e≈1.6×10−19 Coulomb), the electric field E that it generates is inversely proportional to the square of the island size, and may become rather strong for nanoscale structures. For example, the electric field is as large as ˜140 kV/cm on the surface of a 10-nm sphere in vacuum.
The theory of single-electron phenomena shows that a more adequate measure of the strength of these effects is not the electric field, but the charging energy.
 Ec=e2/C  (1)
where C is the capacitance of the island. When the island size becomes comparable with the de Broglie wavelength of the electrons inside the island, their energy quantization becomes substantial. See for instance the articles by: M. A. Kastner, “Artificial Atoms”, Physics Today, vol. 46, pp. 24-31, January 1993; or U. Meirav and E. B. Foxman, “Single-Electron Phenomena In Semiconductors”, Semicond. Sci. Technol. vol. 10, pp. 255-284, October 1995.
In this case the energy scale of the charging effects is given by a more general notion, the electron addition energy Ea. In most cases of interest, Ea may be well approximated by the following simple formula:Ea=Ec+Ek  (2)Wherein EC is given by equation (1) and Ek is the quantum energy of the added electron; for a degenerate electron gas the quantum energy is:Ek=1/g(EF)V  (3)where V is the island volume and g(EF) is the density of states on the Fermi surface.
FIG. 2 shows the total electron addition energy as a function of the island diameter, as calculated using Eq. (2) for a simple but representative model.
For 100-nm-scale devices which were typical for the initial stages of experimental single-electronics, Ea is dominated by the charging energy Ec and is of the order of 1 meV, i.e., ˜10 K in temperature units.
Since thermal fluctuations suppress most single-electron effects unless Ea≧10 kBT, these experiments have to be carried out in the sub-1-K range (typically, using helium dilution refrigerators). On the other hand, if the island size is reduced below ˜10 nm, Ea approaches 100 meV, and some single-electron effects become visible at room temperature.
However, most suggested digital single-electron devices require even higher values of Ea (≈100 kBT) in order to avoid thermally-induced random tunneling events, so that for room temperature operation the electron addition energy Ea has to be as large as a few electron-volts, and the minimum feature size of single-electron devices has to be smaller than ˜1 nm, as shown in the diagram of FIG. 2.
In this FIG. 2 a single-electron addition energy Ea is shown as a solid line, while the charging energy Ec is shown as dashed line and the electron kinetic energy Ek as dotted line, all calculated using Eqs. (1) and (2) for a simple model of a conducting island. In such a model the island is a round 3D ball with a free, degenerate electron gas, embedded into a dielectric matrix (dielectric constant e=4), with 10% of its surface area occupied by tunnel junctions with a barrier thickness d=2 nm. Reference is made to K. K. Likharev, Proc. IEEE, vol. 87, pp. 606-632, April 1999.
In this size range the electron quantization energy Ek becomes comparable with or larger than the charging energy Ec for most materials; this is why islands of these small sizes are frequently called quantum dots. Their use involves not only extremely difficult nanofabrication technology (especially challenging for large scale integration), but also some major physics problems including the high sensitivity of transport properties to small variations of the quantum dot size and shape. This is why it is very important to develop single-electron devices capable of operating with the lowest possible ratio Ea/kBT.
Some examples of single electron devices have been studied and are reported in literature. The following paragraphs will briefly summarize a couple of these devices as state-of-the art technologies for SET, while the article by K. K. Likharev reports the basic theoretical background and physical principles governing the SET functioning.
The simplest device that shows single electron phenomena is the “single-electron box” like that shown in FIG. 3a, and reported by K. K. Likharev. This device comprises just one small island separated from a larger electrode (“electron source”) by a tunnel barrier. An external electric field may be applied to the island using another electrode (“gate”) separated from the island by a thicker insulator, which does not allow noticeable tunneling. The field changes the electrochemical potential of the island and thus determines the conditions of electron tunneling.
This device allowed to verify experimentally the phenomenon, known as “Coulomb staircase”, which is gradually smeared out by thermal fluctuations if the temperature is increased to kBT≈Ec.
Coulomb staircase is a very simple physic phenomenon: increasing gate voltage U attracts more and more electrons to the island. The discreteness of electron transfer through low transparency barriers necessarily makes this increase step-like. Then even such a simple device allows a reliable addition/subtraction of single electrons to/from an island with an enormous (and unknown) number of background electrons, of the order of 1 million in typical low-temperature experiments with 100-nm-scale aluminum islands.
This is of course simply a consequence of the enormous strength of the unscreened Coulomb interaction occurring at low temperatures and, in fact, is the main limitation for the physical implementation of such a kind of single electron devices that are fabricated by scaling down the feature sizes from conventional microelectronics technologies.
Splitting the tunnel junction of the single electron box and applying a dc voltage V between the two, now separate, parts of the external electrode allows obtaining the structure of FIG. 4a. The resulting “single-electron transistor” is probably the most important device in this technical field. In fact, there have been several studies and experimental analysis carried out on this device by some major research organizations in the physics and nanotechnology field.
The expression for the electrostatic energy W of the system is:W=(ne−Qe)2/2CΣ−eV[n1C1+n2C2]+const  (4)Here n1 and n2 are the number of electrons passed through the tunnel barriers 1 and 2, respectively, so that n=n1−n2, while the total island capacitance CΣ is now a sum of C0, C1, C2, and whatever stray capacitance the island may have. The external charge Qe is defined by the equationQe=UC0  (5)and is just a convenient way to present the effect of the gate voltage U.
Capacitive-coupled single-electron transistor: (a) schema, (b) source-drain dc I-V curves of a symmetric transistor for several values of the Qe, i.e., of the gate voltage, and (c) the Coulomb blockade threshold voltage Vt as a function of Qe at T→0.
FIG. 4b shows typical dc I-V curves of this system. At small source-drain voltage Vt there is no current, since any tunneling event would lead to an increase of the total energy (ΔW<0) and hence at low enough temperatures (kBT<<Ec) the tunneling rate is exponentially low. This suppression of dc current at low voltages is known as the Coulomb blockade. At a certain threshold voltage Vt the Coulomb blockade is overcome, and at much higher voltages the dc I-V curve gradually approaches one of the offset linear asymptotes:I→(V+sign(V)·(e/2CΣ))/(R1+R2)
On its way, the I-V curve exhibits quasi-periodic oscillations of its slope, closely related in nature to the Coulomb staircase in the single-electron box, and expressed especially strongly in the case of a strong difference between R1 and R2.
The most important property of the single-electron transistor is that the threshold voltage, as well as the source-drain current in its vicinity, is a periodic function of the gate voltage. This periodicity is evident from Eqs. (4) and (5): if U is changed by ΔU=e/C0, Qe changes by e, and may be exactly compensated for by one of the electrons tunneling into or from the island.
As the transistor island becomes smaller, the effects of energy quantization may become important. The theory shows that its dc I-V curves may be quite complex, as disclosed by D. V. Averin, A. N. Korotkov, and K. K. Likharev, “Theory Of Single-Electron Charging Of Quantum Wells And Dots”, Phys. Rev. B, vol. 44, pp. 6199-6211, September 1991.
However, the situation at small source-drain voltage is much simpler. In fact, FIG. 4c shows that on each period of the Coulomb blockade oscillations there is one special point:Qe=e(n+½)at which the Coulomb blockade is completely suppressed, and the I-V curve has a finite slope at low voltages (see FIG. 4b).
Another way to express the same property is to say that the linear conductance G=dI/dV|V=0 of the transistor as a function of the gate U voltage exhibits sharp peaks. Theory shows that even if the electron quantization effects are substantial, the peak position may be found from a very natural “resonance tunneling” condition as disclosed by H. van Houten, C. W. J. Beenakker, and A. A. A. Staring, “Coulomb Blockade Oscillations In Semiconductor Nanostructures”, in: Single Charge Tunneling, ed. by H. Grabert and M. H. Devoret. New York: Plenum, 1992, pp. 167-216; and by C. W. J. Beenakker, “Theory of Coulomb-blockade oscillations in the conductance of a quantum dot”, Phys. Rev. B, vol. 44, pp. 1646-1656, July 1991.
So, an energy level inside the island (with the account of the gate field potential) should be aligned with the Fermi levels in source and drain, which coincide at V→0. This rule yields a simple equation for the gate voltage distance between the neighboring Coulomb blockade peaks:ΔU=(CΣ/C0)Ea/e  (6)Fabrication of SET promotes many difficulties for this device to be used in a large scale industrial production, since:                It is vitally important to develop technologies to realize nanoscale Quantum Dots (QD) and quantum wires, which are coupled together through tunneling barrier, and which must be precisely controlled in their size and position.        Process induced damage and contamination must be avoided in the fabrication of large scale SET circuits.        The technique must have high reproducibility and controllability.        
Basically the fabrication methods can be divided as physical or chemical techniques according to the main procedures.
The physical methods often utilize the combination of thin film and lithographic technologies.
Devices with carefully tailored geometries and electron density are obtained. For example, quantum dots or quasi-zero-dimensional puddles of electrons with weak coupling to simultaneously patterned electrical leads are fabricated to form a SET. However, lithographic and materials limitations restrict the minimum size and composition of such dots (100 nm), and studies are typically limited to sub-Kelvin temperatures.
Another possible approach is to grow nanostructures chemically as reported by David L. Klein, Paul L. McEuen, etc., in Appl. Phys. Lett., v68, 1996, p2575.
This approach is prosperous for its low cost and good controllability of the size of Coulomb islands, and it is possible to be a prospective technique.
Though this technique is not mature industrially, the SETs fabricated in laboratories show fascinating results.
Generally there are three most important steps:                first, the fabrication of Coulomb islands as well as the control of their size and dispersity;        second, the formation of tunneling junctions at the joint of electrodes and Coulomb island;        third, the formation of gate between substrate and Coulomb islands.        